Question

Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft.^3 . They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh , rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V in the formula

Answer 1

To find the width (w) of the cabinet using the volume formula, we start with the formula for volume:

\[ V = l \cdot w \cdot h \]

Where:
- \( V \) is the volume,
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

We are given:
- \( V = 60 \, \text{ft}^3 \)
- \( l = 4 \, \text{ft} \)
- \( h = 5 \, \text{ft} \)

We want to rearrange the formula to solve for the width \( w \). We can do this by isolating \( w \) on one side of the equation.

Starting with the original equation:

\[ V = l \cdot w \cdot h \]

We can divide both sides by \( l \cdot h \):

\[ w = \frac{V}{l \cdot h} \]

Now substituting in the values for \( V \), \( l \), and \( h \):

\[ w = \frac{60 \, \text{ft}^3}{4 \, \text{ft} \cdot 5 \, \text{ft}} \]

Calculating the denominator:

\[ 4 \, \text{ft} \cdot 5 \, \text{ft} = 20 \, \text{ft}^2 \]

Now substituting that back into the equation for \( w \):

\[ w = \frac{60 \, \text{ft}^3}{20 \, \text{ft}^2} \]

Calculating \( w \):

\[ w = 3 \, \text{ft} \]

Thus, the width of the cabinet is **3 ft**.